The claim defended in the paper is that the mechanistic account of explanation can easily embrace idealization in big-scale brain simulations, and that only causally relevant detail should be present in explanatory models. The claim is illustrated with two methodologically different models: Blue Brain, used for particular simulations of the cortical column in hybrid models, and Eliasmith’s SPAUN model that is both biologically realistic and able to explain eight different tasks. By drawing on the mechanistic theory of computational explanation, (...) I argue that large-scale simulations require that the explanandum phenomenon is identified; otherwise, the explanatory value of such explanations is difficult to establish, and testing the model empirically by comparing its behavior with the explanandum remains practically impossible. The completeness of the explanation, and hence of the explanatory value of the explanatory model, is to be assessed vis-à-vis the explanandum phenomenon, which is not to be conflated with raw observational data and may be idealized. I argue that idealizations, which include building models of a single phenomenon displayed by multi-functional mechanisms, lumping together multiple factors in a single causal variable, simplifying the causal structure of the mechanisms, and multi-model integration, are indispensable for complex systems such as brains; otherwise, the model may be as complex as the explanandum phenomenon, which would make it prone to so-called Bonini paradox. I conclude by enumerating dimensions of empirical validation of explanatory models according to new mechanism, which are given in a form of a “checklist” for a modeler. (shrink)

Endowing artificial systems with explanatory capacities about the reasons guiding their decisions, represents a crucial challenge and research objective in the current fields of Artificial Intelligence (AI) and Computational Cognitive Science [Langley et al., 2017]. Current mainstream AI systems, in fact, despite the enormous progresses reached in specific tasks, mostly fail to provide a transparent account of the reasons determining their behavior (both in cases of a successful or unsuccessful output). This is due to the fact that the classical problem (...) of opacity in artificial neural networks (ANNs) explodes with the adoption of current Deep Learning techniques [LeCun, Bengio, Hinton, 2015]. In this paper we argue that the explanatory deficit of such techniques represents an important problem, that limits their adoption in the cognitive modelling and computational cognitive science arena. In particular we will show how the current attempts of providing explanations of the deep nets behaviour (see e.g. [Ritter et al. 2017] are not satisfactory. As a possibile way out to this problem, we present two different research strategies. The first strategy aims at dealing with the opacity problem by providing a more abstract interpretation of neural mechanisms and representations. This approach is adopted, for example, by the biologically inspired SPAUN architecture [Eliasmith et al., 2012] and by other proposals suggesting, for example, the interpretation of neural networks in terms of the Conceptual Spaces framework [Gärdenfors 2000, Lieto, Chella and Frixione, 2017]. All such proposals presuppose that the neural level of representation can be considered somehow irrelevant for attacking the problem of explanation [Lieto, Lebiere and Oltramari, 2017]. In our opinion, pursuing this research direction can still preserve the use of deep learning techniques in artificial cognitive models provided that novel and additional results in terms of “transparency” are obtained. The second strategy is somehow at odds with respect to the previous one and tries to address the explanatory issue by avoiding to directly solve the “opacity” problem. In this case, the idea is that one of resorting to pre-compiled plausible explanatory models of the word used in combination with deep-nets (see e.g. [Augello et al. 2017]). We argue that this research agenda, even if does not directly fits the explanatory needs of Computational Cognitive Science, can still be useful to provide results in the area of applied AI aiming at shedding light on the models of interaction between low level and high level tasks (e.g. between perceptual categorization and explanantion) in artificial systems. (shrink)

The paper discusses some changes in Bolzano's definition of mathematics attested in several quotations from the Beyträge, Wissenschaftslehre and Grössenlehre: is mathematics a theory of forms or a theory of quantities? Several issues that are maintained throughout Bolzano's works are distinguished from others that were accepted in the Beyträge and abandoned in the Grössenlehre. Changes are interpreted as a consequence of the new logical theory of truth introduced in the Wissenschaftslehre, but also as a consequence of the overcome of Kant's (...) terminology, and of the radicalization of Bolzano's anti‐Kantianism. Bolzano's evolution is understood as a coherent move, once the criticism expressed in the Beyträge on the notion of quantity is compared with a different and larger notion of quantity that Bolzano developed already in 1816. This discussion is enriched by the discovery that two unknown texts mentioned by Bolzano in the Beyträge can be identified with works by von Spaun and Vieth respectively. Bolzano's evolution is interpreted as a radicalization of the criticism of the Kantian definition of mathematics and as an effect of Bolzano's unaltered interest in the Leibnizian notion of mathesis universalis. As a conclusion, the author claims that Bolzano never abandoned his original idea of considering mathematics as a scientia universalis, i.e. as the science of quantities in general, and suggests that the question of ideal elements in mathematics, apart from being a main reason for the development of a new logical theory, can also be considered as a main reason for developing a different definition of quantity. (shrink)